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Imagine a scenario: On a stand, an $RC$ plane motor is mounted on a stand. The motor has a $8x4$ prop attached to it. In the theoretical model, if the spin of the motor can be increased infinitely without burning it out,

  • will the wind it produces towards the back as the propeller spins always increase or will it plateau over time?

Could you answer this question in the real world. Which means, what would happen in real world taking all phenomena into effect such as friction, air resistance and other related phenomena.

  • Whatever the answer, is there an authoritative source that can be provided which I can cite?

Thank You

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    $\begingroup$ The model you are proposing is ofcourse to unrealistic to account for what happens at high rotation speeds. Even if the rotors didn't break at high speeds (which they surely will) you will eventually run into problems with special relativity, limiting the maximum speed. $\endgroup$ – Mikael Fremling Jan 8 '16 at 9:35
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    $\begingroup$ The question looks fine to me. It's basically asking if there is a maximum speed above which a fan doesn't work, and the answer is yes it's when the blade speed exceeds the speed of sound. $\endgroup$ – John Rennie Jan 8 '16 at 9:45
  • $\begingroup$ See en.wikipedia.org/wiki/… $\endgroup$ – RedGrittyBrick Jan 8 '16 at 17:00
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In order for a fan or prop blade to deflect air backwards, there has to be air where the fan blade is, obviously. A fan pushes air, and pushing is something that requires physical contact.

Wind speed is a measure of the average relative motion of the individual molecules of the air itself: at any given time in an atmosphere there are molecules going every which way at various speeds, but if there are more going one direction than another, or if the ones going that direction tend to be faster, then there is a wind. That's how a fan blade generates wind - it takes the air molecules and shoves them in a particular direction.

"It takes air molecules" is deliberately phrased, because in order for a fan to blow air, it has to get air to blow. Imagine you put your fan into a bucket of water and it starts 'blowing' the water out of the bucket: once the bucket is empty, the fan stops blowing water because there's no more water to blow.

The same thing happens with a fan: if your fan blades are going too quickly, one blade will scoop up all the air and blow it away, but by the time the second blade comes aroung, the only molecules that are there for it to catch are the ones that were already going that direction. Naturally, these are moving at a variety of speeds around an average in that direction, and the faster they're going already, the less energy the fan blade can impart to them. There is then a plateau effect in which there's a maximum speed that the fan blade can push air out, and that speed coincides with the speed of sound in that medium, I.e. the speed the molecules were already going naturally.

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